Optimality Conditions and a Method of Centers for Minimax Fractional Programs with Difference of Convex Functions

Karima Boufi (), Mostafa El Haffari () and Ahmed Roubi ()
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Karima Boufi: Univ. Hassan 1
Mostafa El Haffari: Univ. Abdelmalek Essaâdi
Ahmed Roubi: Univ. Hassan 1

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 1, No 6, 105-132

Abstract: Abstract We are concerned in this paper with minimax fractional programs whose objective functions are the maximum of finite ratios of difference of convex functions, with constraints also described by difference of convex functions. Like Dinkelbach-type algorithms, the method of centers for generalized fractional programs fails to work for such problems, since the parametric subproblems may be nonconvex, whereas the latters need a global optimal solution for these subproblems. We first give necessary optimality conditions for these problems, by means of convex analysis tools, and then extend the last method to solve such programs. The method is based on solving a sequence of parametric convex problems. We show that every cluster point of the sequence of optimal solutions of these subproblems satisfies necessary optimality conditions of Karush–Kuhn–Tucker criticality type.

Keywords: Fractional programming; Difference of convex functions; Optimality conditions; Method of centers; 90C32; 90C26; 90C25; 90C47; 90C46 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01738-2

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